In poker, you make a pocket pair when the ranks of your first two cards match. This does not include making a pair on the flop or in a full 7-card hand.
There are six ways to draw a pocket pair of a given rank, but how many ways are there to draw any pocket pair, and what are the odds of doing so?
Footnotes
Posting as an answer for my own reference, and because the Poker StackExchange question did not support LaTeX.
Not a duplicate: While there are other questions on MSE related to flopping a pair or making one in a full 7-card hand, this question is limited to just pocket pairs (your private 2-card hand).
Any pocket pair will consist of one rank and two suits. Thus, there are $\dbinom 4 2 = 6$ ways to choose 2 suits from the 4 suits of a given rank, and $\dbinom {4}{2}\dbinom{13}{1} = 78$ ways to choose a pocket pair from all 13 ranks.
Because there are $\dbinom{52}{2} = 1326$ ways to choose any 2-card hand from a 52-card deck, the probability of drawing a pocket pair is:
$$ \frac{\dbinom {4}{2}\dbinom{13}{1}}{\dbinom{52}{2}} = \frac{78}{1326} = \frac{3}{51} = 5.8823\% \text{ (16:1 odds)} $$
This simplifies to $\frac{3}{51}$ because given any first card from the deck, 3 cards in the remaining deck of 51 complete the pocket pair.